Lab 10: Polarization Phy248 Spring 2009

Transcription

1 Lab 10: Polarization Ph248 Spring 2009 Name Section This sheet is the lab document our TA will use to score our lab. It is to be turned in at the end of lab. To receive full credit ou must use complete sentences and eplain our reasoning clearl. What s this lab about? In this lab ou investigate effects arising when using polarized light. There are four parts to the lab: PART A Use a polarizer to eplore common occurrences of polarized light PART B Use a polariscope to understand how polarized light waves can be superposed, or decomposed into components. PART C Create and investigate circular polarization. PART D Use the ideas of circular polarization and superposition to see how polarized light interacts with biological sugar molecules. Wh are we doing this? Understanding polarized light is important applications such as microscop, as well as in understanding the properties of electromagnetic waves. What should I be thinking about before I start this lab? Suppose an electromagnetic wave is propagating through our area at the speed of light. If ou could take a snapshot, ou could freeze the electric and magnetic fields at a particular instant in time so that ou could look at them. At each point in space around ou, and at each instant in time, ou would see electric and magnetic fields with these properties: i) E r and B r are alwas perpendicular to each other, and also to the wave propagation direction (such that E r " B r is in the propagation direction) ii) The magnitudes E r " E and B r " B are related as B( o, o,z o,t o ) = ( 1/c)E( o, o,z o,t o ). iii) r E and r B both oscillate in time with a frequenc f = v /" (v is the propagation speed) iv) It takes a time T=1/f (the period) for the fields to complete one complete ccle at a fied point in space, and a distance λ (the wavelength) to complete one complete ccle at a fied time.

2 A. Making and detecting polarized electromagnetic waves In a linearl polarized electromagnetic wave, the electric field varies in time and space, but it alwas lies in a plane of polarization. Since the associated magnetic field is alwas perpendicular to this, we can describe the polarization completel b describing the orientation of the electric field. Light doesn t often look like this unless it is speciall prepared. It is usuall a superposition of all possible polarizations, which we call unpolarized light. A linear polarizer can be used to investigate the polarization state. It completel transmits linearl polarized light aligned with its transmission ais, and completel absorbs light linearl polarized perpendicular to its transmission ais. 1. Polarization b reflection. Light is partiall polarized whenever it is reflected. You can check this b using the linear polarizer from the polarization kit on the lab table. Raised lines on the black plastic disc that holds the polarizing material mark the transmission ais. i) First look through the polarizer directl at the black desklamp on our lab bench. Does the desklamp produce polarized light? How did ou tell? ii) Now aim the lamp at the lab bench at about a 30 to 45 angle (from the horizontal), and look through the polarizer at the reflection of the bulb. Is this light polarized? In what direction is the plane of polarization? iii) Polaroid sunglasses operate on the same principle as our kit polarizer. In what direction is the transmission ais of Polaroid sunglasses? Eplain. iv) Use our polarizer to look at our cell-phone displa or a computer LCD monitor. Describe the light emitted b these. 2

3 The polariscope Your polariscope has two polarizers (even though one is called an analzer!): The bottom one sits directl over the (unpolarized) incandescent bulb, and is fied in place. In a twopolarizer sstem, it is usuall called the polarizer, since it produces linear polarized light from an unpolarized source. The top one can rotate. It is usuall in-line with the bottom polarizer, but can also be swung to the side. In a twopolarizer sstem, it is usuall called the analzer, since it analzes whether a sample placed above the bottom polarizer has altered the polarization. Analzer Polarizer Unpolaized light Rotate 1. Turn on our polariscope and look down into the top polarizer. Describe the intensit variations while rotating the top polarizer through Find the transmission ais of the bottom polarizer with the small polarizer (mounted in a black plastic ring) from our bo. This one has its transmission ais marked with two ridges in the plastic. Eplain our procedure and use a piece of masking tape to mark it on the rim of the polariscope. Find the transmission ais of the top polarizer and mark it also. 3. What angle is between the transmission aes of the two polarizers when there is: Maimum transmission? What about no transmission? 3

4 B. Transmission through a polarizer: In the previous section, ou found that a linear polarizer will transmit a light wave whose electric field vector is parallel to the transmission ais, and blocks (absorbs) one with electric field vector perpendicular to that direction. For angles not 0º or 90º with respect to the transmission ais the polarizer transmits the component of the E-field along the transmission ais and absorbs the rest. B1. Set the analzer on our polariscope so that no light is transmitted. Now insert the small round polarizer from our kit between them and rotate it. Unpolaized light Kit polarizer Wh does light now get through at some angles? B2. Rotate the middle polarizer through a full 360. From our eperimental observations, qualitativel sketch the intensit through the top analzer vs angle of the middle polarizer transmission ais relative to the transmission ais of the bottom fied polarizer B3. At what angles of the inner polarizer do ou get maimum intensit? Eplain. 4

5 C. Circular Polarization: An important tpe of polarization occurs when two plane-polarized waves are added together. One wave is time-delaed b one quarter of a period (a 90 phase shift). In the figure the horizontal EM wave starts later in time. (Onl the E-fields of the two EM waves are shown). 1. The graphs below show the E-fields of the two linearl-polarized waves at time intervals Δt=T/8 (T is the wave period). The wave polarized along the -ais starts later in time. Draw the vector sum of the two E-fields on each plot. 0 T/8 2T/8 3T/8 4T/8 5T/8 t=0 t=t/8 t=2t/8 t=3t/8 t=4t/8 t=5t/8 t=6t/8 t=7t/8 t=t 5

6 2. Describe the time-dependence of the total E-field (direction and magnitude). Does the magnitude change in time? Does the direction change in time? When the horizontal component starts ¼ period earlier (-90 phase shift) rather than later, the electric field vector rotates in the opposite direction. These two polarization states are right and left circular. Making circularl polarized light As ou showed above, ou can make circularl polarized light b combining two linearl polarized waves, with their plane of polarizations at right angles, and with a relative dela of ¼ wavelength. There is a ver eas wa to do this. Some materials are opticall anisotropic, meaning that light waves polarized along different directions travel at different speeds. This means that the slower one is delaed relative to the faster one. You have two of these in our plastic bo. The thickness of the plate is such that the time dela is ¼ of the wave oscillation period T ( equivalent to a ¼ wavelength dela, or 90 in phase). These are called ¼-wave plates. 3. You have ¼ wave plate in our kit made from quartz. It gives eactl ¼ wavelength dela between the fast and slow aes for 540 nm wavelength light. The inde of refraction along the slow ais is n slow =1.5, and along the Fast ais fast ais is n fast = a) What is the propagation speed? i) along the slow ais? ii) along the fast ais? b) How thick must the plate be so that the wave along the slow ais takes T/4 seconds longer to make it through the waveplate than the wave along the fast ais? Here T is the oscillation period of 540 nm light in vacuum. [Hint: if the waveplate thickness is L, how man seconds does it take for the slow wave to travel through the waveplate? The fast wave?] Slow ais 6

7 Analzing circular polarization: Set the ¼ wave plate on the lower polarizer of the polariscope. Align the wave plate so that the linearl polarized light enters with its plane of polarization halfwa between the fast and slow aes of the ¼ wave plate. (The fast ais is marked on the brass holder) Now - and -components of the linearl polarized light have equal amplitude, and are aligned with the fast and slow aes of the ¼ wave plate. Fast ais Transmission ais ¼ wave plate Linear polarizer Slow ais 4. Eplain wh this should produce circularl-polarized light. 5. Now rotate the top polarizer. The intensit of the light transmitted through the wave plate remains approimatel constant as ou rotate the analzer (top polarizer) [ou ma need to slightl adjust the wave-plate angle]. Eplain wh this happens. 7

8 D. Chiral molecules and polarized light We discuss circular polarization because man molecules interact differentl with left-handed and right-handed light due to their molecular chiralit, or handedness. Amino acids (shown at right in both chiralities) and sugars are chiral. Your bod uses and produces onl D-sugars (right-handed) and onl L- amino acids (left-handed). 1. Eplain wh the molecules in the figure above are not identical. In a biological (right-handed) sugar solution, right and left circularl polarized light interact differentl with the right-handed molecules. The result is that the EM waves propagate at different speeds. To observe this, we could have a race between right- and left-circularl polarized light. We would start them at the same time, and see which one arrived first at the other end of the sugar solution. Sounds complicated, but it turns out that right- and left-circularl polarized light together is something ou ve seen before: 2. Below are plots that let ou superimpose two EM waves with right and left circular polarizations. At t o both have their E-fields pointing along the -ais (i.e. the are in phase with each other). As time progresses, one rotates clockwise and the other counter-clockwise. Add the E-fields as vectors as ou did the two linear polarizations in C1. Draw the resultant vector at each time step. t o t 1 t 2 t 3 t 4 t 5 Describe the polarization of the EM wave that is the sum of these two circularl polarized waves. Is it circularl polarized? Linearl polarized? How does the electric field point? 8

9 This means that ou can race right- and left- circularl polarized light through a chiral solution b sending in linearl polarized light. In D2 above, the right and left-circularl polarized light start together (in-phase), read to race. But the propagate at different speeds, so that one will arrive sooner at the other end. This results in a relative dela between right- and left- circular polarization when the leave the chiral solution. 3. Below are plots that let ou superimpose the electric field vectors of right and left circularl polarized EM waves with a relative dela. The left-handed light is delaed (" left # " right )=90 (1/4 period) from the right-handed light. Add the E-fields as vectors as ou did in D2. Draw the resultant vector at each time step. t o t 1 t 2 t 3 t 4 t 5 Describe the polarization of the sum of these two circularl polarized waves. 4. The relation between the polarization angle θ of the resulting linear polarization, and the relative phase dela " left # " right between the left- and right-handed polarization components, is " pol = # left $ # right made in D2 and D3. ( ) /2. Eplain how this is consistent with the plots ou 9

10 Now ou do the eperiment, sending linearl polarized light through a concentrated biological sugar solution. We use Karo corn srup because it is a ver concentrated chiral solution of right-handed molecules (sugars) onl. If ou don t know what Karo srup is, call our mother and ask her. She probabl hasn t heard from ou in a while, and would enjo talking with ou. The right- and left-circularl polarized components of the linearl polarized light propagate at different speeds. The start at the same time, but arrive at the other end with a relative dela, which ou just showed appears as rotated linearl polarized light. Get a set of four jars of Karo srup (three small and one large, with different heights of srup). Don t tip them: the srup takes time to run back down into the jar. 5. Place the large jar (lid off, open end up) on the polarizer and rotate the analzer while looking through the polarizers and srup. You should see colors in the srup. In what order do the colors appear as ou rotate the analzer clockwise? Since the rotation appears to be different for different colors (wavelengths), place a color filter (colored transparenc) under the srup so ou are onl looking at one color (see spectral transmission below). TRANSMISSION ( % ) Roscolu #122, Green Diffusion TRANSMISSION ( % ) WAVELENGTH ( nm ) WAVELENGTH ( nm ) Rotate the analzer so the light outside the jar but through the filter is etinguished. Then rotate the analzer until the light through the srup is etinguished. The difference of these angles is the angle b which the Karo has rotated the light. 6. What direction (clockwise or counter-clockwise, looking from the top) is the plane of polarization rotated? How did ou tell? (Hint: a little bit of Karo rotates the polarization a little bit, and a lot rotates it more, so look at the jar with a little Karo) Roscolu #124, Red Cc Silk 10

11 Record the polarization rotation of the large jar for the red and green filters. Filter color: Relative rotation (deg): 7. Do this for the other jars and record all our data below. Sugar depth Green angle Red angle 8. Plot the data for the two colors on the aes below. 140 Polarization Rotation (deg) Sugar Depth (cm) 11

12 Now ou analze the data, first using an approimate value for the velocit ratios in order to develop the concepts. 9. Suppose that the right-handed component moves at the speed of the lefthanded component (v right /v left = ). Then the left-handed component arrives at the top of the srup a short time "t before the right-handed component. What is "t after traversing 8 cm of Karo? (take v left = c = 3"108 m /s = 2 "10 8 m /s). n Karo 1.5 The phase difference between the right- and left-handed components depends on the arrival time difference "t and on the oscillation period T. For instance "t = T /2 corresponds to a phase shift of π (180 ). "t = T /4 gives a phase shift of π/2 (90 ). 10. The peak wavelength of red light ou used above is about 660 nm in vacuum. This has an oscillation period T = " /c = 2.20 #10 $15 s. What is the phase difference " left # " right between the left- and right-handed components for the time dela "t calculated in D9? 11. The peak wavelength of green light ou used above is about 520 nm in vacuum. This has an oscillation period of T = " /c =1.73 #10 $15 s What is the phase difference " left # " right between the left- and right-handed components for the time dela "t calculated in D9? 12. Using " pol = (# left $ # right ) /2 from D4, what polarization rotations are these? Red Light rotation: Green Light rotation: 12

13 13. Wh did the same arrival time difference result in different polarization rotations for different colors of light? 14. Eplain whether our answer to the question above describes the order of the colors ou observed in D5, assuming that the arrival time dela does not depend on wavelength. 15. Now ou use our measurements of rotation angle to determine the ratio of rightand left-handed polarization velocities in the right-handed sugar solution. i) Using our data for polarization rotation through 8 cm of Karo, calculate the difference in arrival time "t for the left- and right-handed components. Red light "t Green light "t ii) From D9-12, ou should epect that v right is just a little smaller than v left. Again taking v left = c /n Karo = 2 "10 8 m /s, determine v right /v left from our "t in i) above. Red light v right /v left Green light v right /v left iii) Qualitativel, how did this etremel small speed difference show up as such a large polarization rotation? 13